Application of the CIR model for spot short interest rates modelling on the polish market

Abstract

The paper examines the estimation of the instantaneous Polish short term interest rate using one of the most popular stochastic differential models for studying the short interest rates, i.e. the Cox, Ingersoll, Ross model (1985) (henceforth CIR). We propose a new approach to estimating an instantaneous short interest rate: our attention is shifted from the whole term structure of the interest rate to the artificial notation of the short rate. In particular, the method focusing on determining a relationship between an observed instantaneous short interest rate and a certain (abstract) unobserved instantaneous rate which is defined as an interest rate demanded over an infinitesimally short period under the risk-neutral measure. To estimate the CIR model, we use a state space model in which estimates of the latent variables and model parameters are obtained by applying an Expectation-Maximisation algorithm combined with particle filters (PF). In practice, the instantaneous rate is identified with an overnight rate, therefore during the research we have adopted daily domestic interbank lending rates which are represented by interest rates on overnight deposits (WIBOR ON). To facilitate the discussion, simulated data are also employed. The obtained results prove the correctness and attractiveness of the method under consideration.